Universality class of one-dimensional directed sandpile models.

@article{Stapleton2005UniversalityCO,
  title={Universality class of one-dimensional directed sandpile models.},
  author={Matthew Stapleton and Kim Christensen},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2005},
  volume={72 6 Pt 2},
  pages={066103}
}
A general n-state directed "sandpile" model is introduced. The stationary properties of the n-state model are derived for n<infinity, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed… CONTINUE READING